First : no, København is not the capital of Sweden or Scandinavia, but of Danmark, called "Denmark" in English.
I'm explaining this basic stuff because sometimes I'm surprised by how little foreigners (Americans for example) know about Danmark--but then again, I travelled to Prague for the first time this year, and must admit that I knew just as little about the Czechs, an entire culture of millions of people who simply haven't registered in my consciousness because I've had absolutely no contact with them. Their country was a blank spot on my mental map, just as Afghanistan had been before I'd travelled through there.
But of course, everybody knows about the Vikings, and the cheese, and the furniture design, and the (oh boy!) Free Sex, so they DO have some picture of "Danes" somewhere in their heads, right or wrong.
Anyway, Danmark is the European / Scandinavian country just north of Germany, composed of one peninsula and lots of islands--500 of 'em--most quite small, but the largest is Sjælland, where København perches on the east coast. They say that if you were to string all of the coastlines together into a straight line they would reach a third of the way around the planet...but the truth is that Danmark is a little country. And that's what's nice about it.
Pre-21st Century you had to sail to Sjælland, either from Jutland or Germany or Sweden, which had been fairly easy to do, there having been a well-developed ferryboat system, but in 1999 the Storbælts Bridge was built, suddenly physically connecting København with mainland Europe all the way to Gibraltar.
The Øresunds Bridge was finished two years later and now we're connected from Gibraltar to Nord Cap, up in the Artic Circle. In more practical usage we can drive a car from Kbh to Malmö, or take the new Metro over, a 20 minute trip. This has transformed the entire København -Malmö area to a greater metropolitan hub, wherein commuters travel both ways for jobs and housing.
Next bridge coming up is the Fehmur connection with Germany. So big changes are happening right now; Danmark is no longer a cluster of islands unto itself.